Derousseau's Generalization of the Malfatti circles

\(a:b:c=5:12:13\).

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[Other solutions]
[Guy]
[Lob & Richmond]

\(\mathbf{3b}\) \((123)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&1.278649238600&{}:{}&3.343790863202&{}:{}&-3.622440101802&,\\B^\prime&{}\approx{}&-0.249218138163&{}:{}&1.897185297387&{}:{}&-0.647967159224&,\\C^\prime&{}\approx{}&-2.306997126177&{}:{}&5.536793102824&{}:{}&-2.229795976647&. \end{alignedat} \]
3b (123)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}-1.671895431601\overrightarrow{AI_B},\\\overrightarrow{BB^\prime}&\approx{}-0.299061765796\overrightarrow{BI_B},\\\overrightarrow{CC^\prime}&\approx{}-2.768396551412\overrightarrow{CI_B}. \end{aligned} \] \[ \begin{alignedat}{4} I_B&{}\approx{}&0.833333333333&{}:{}&-2.000000000000&{}:{}&2.166666666667&. \end{alignedat} \]
3b (123)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&-0.182661048441&{}:{}&3.122132208906&{}:{}&-1.939471160465&. \end{alignedat} \]
3b (123)

Hiroyasu Kamo